MIME type for a directory

There is no universal answer to this question.

Directories are not considered to have MIME types on Windows.

On Android, the directories exposed by a document provider are of type "vnd.android.document/directory" while those exposed by other content providers are typically of the form "vnd.android.cursor.dir/<something>".

On Linux, the xdg shared mime info spec dictates "inode/directory" be used for associating directories with applications.

On Ubuntu, a directory mimetype is inode/directory

If you run, on Ubuntu:

$ mimetype /home/<your username>
/home/<your username>: inode/directory

There is a "text/directory" in the IANA standards (http://www.rfc-editor.org/rfc/rfc2425.txt and http://www.iana.org/assignments/media-types/text) but it was marked "deprecated".